Photovoltaic energy extraction with multilevel output dc-dc switched capacitor converters

ABSTRACT

Switched capacitor multilevel output DC-DC converters can be used as panel integrated modules in a solar maximum power point tracking system. The system can also include a central input current-controlled ripple port inverter. The system can implement per panel MPPT without inter-panel communication, electrolytic capacitors or per panel magnetics. A Marx converter implementation of the switched capacitor module is studied. Average total efficiencies (tracking×conversion) greater than 93% can be achieved for a simulated 510 W, 3 panel, DC-DC system.

STATEMENT OF GOVERNMENT SUPPORT

This invention was made with government support under Grant No.DE-SC0002231 awarded by the Department of Energy. The government hascertain rights in this invention.

BACKGROUND

1. Technical Field

The techniques described herein relate to photovoltaic systems, powerconverters, associated circuits and related techniques for extractingenergy from photovoltaic panels.

2. Discussion of the Related Art

There are several factors limiting the widespread adoption of solarpower. The total installed cost ($/W) and total cost of ownership ($/Wh)have been well-studied as key metrics controlling grid penetration.Among the factors impacting installed cost per Watt are power convertercost and system efficiency, both of which share strong relations toconverter and system complexity. A significant factor impacting the costof ownership is the lifetime of the power converter and associatedreplacement costs. Cost-effective solutions for solar energy extractionshould address system cost and complexity, conversion and trackingefficiencies and converter lifetimes.

The amount of power extracted from a photovoltaic (PV) module dependsupon the operating point at which the PV module is operated. The amountof power extracted from the PV module is optimized when the product ofthe current and voltage at the output of the PV module is maximized. Toextract the maximum amount of power from the PV panel, the current andvoltage at the output of the PV panel can be set so that the PV paneloperates at its maximum power point. However, the maximum power pointcan change over time, due to factors such as the amount of sunlightreceived and the age of the PV panel. A maximum power point tracking(MPPT) algorithm embedded in the control of a converter or an invertercan be used to control the power electronics so that the current andvoltage at the PV module tracks the maximum power point.

In a grid-tied system, 120 Hz power ripple at the PV panel terminalsnegatively impacts the tracking ability of the MPPT algorithm. Thisproblem may be addressed by adding a large electrolytic capacitor tofilter out the ripple. However, the limited lifetime of electrolyticcapacitors contends directly with the long-life characteristic desiredfor cost-effective solar conversion. To reconcile this, the “rippleport” inverter has been proposed, which still directly interfaces withthe PV unit, but directs the 120 Hz ripple power to atransformer-coupled ripple port and away from the PV unit.

SUMMARY

Some embodiments relate to a circuit for obtaining power from aphotovoltaic unit. The circuit includes a DC-DC power converterconfigured to convert a first signal from the photovoltaic unit into asecond signal using a conversion ratio selected from a set of discreteconversion ratios that the DC-DC power converter is capable ofproviding.

Some embodiments relate to a circuit that includes a multi-level outputDC-DC switched capacitor power converter configured to receive a firstsignal from a photovoltaic unit and to convert the first signal into asecond signal. The circuit also includes a controller configured tocontrol the multi-level output DC-DC switched capacitor power converterusing a maximum power point tracking algorithm.

Some embodiments relate to a circuit for controlling a photovoltaicsystem. The circuit includes a plurality of series-connected moduleintegrated converters. Each module integrated converter includes amulti-level output DC-DC switched capacitor power converter coupled to aphotovoltaic module and a first controller configured to control themulti-level output DC-DC switched capacitor power converter using amaximum power point tracking algorithm. The circuit also includes aninverter coupled to the plurality of series-connected module integratedconverters. The inverter includes a second controller to control acurrent through the plurality of series-connected module integratedconverters.

Some embodiments relate to a system for controlling a plurality ofphotovoltaic units. The system includes a first power converter coupledto a first photovoltaic unit and a first controller to control the firstpower converter to operate the first photovoltaic unit using a maximumpower point tracking algorithm. The system also includes a second powerconverter in series with the first power converter and coupled to asecond photovoltaic unit and a second controller to control the secondpower converter to operate the second photovoltaic unit using a maximumpower point tracking algorithm. The system further includes a thirdcontroller that controls a current through the first and second powerconverters.

Some embodiments relate to a gate drive circuit that includes a levelshift circuit and a charge pump circuit. The charge pump circuitprovides a floating gate drive voltage to a transistor of a multileveloutput DC-DC switched capacitor power converter based on a signal fromthe level shift circuit.

The foregoing summary of some embodiments is provided by way ofillustration and is not intended to be limiting.

BRIEF DESCRIPTION OF DRAWINGS

In the drawings, each identical or nearly identical component that isillustrated in various figures is represented by a like referencecharacter. For purposes of clarity, not every component may be labeledin every drawing. The drawings are not necessarily drawn to scale, withemphasis instead being placed on illustrating various aspects of theinvention.

FIG. 1 a shows an example of a PV system, according to some embodiments.

FIG. 1 b shows an example of a PV module.

FIG. 1 c shows an example of a module integrated converter (MIC),according to some embodiments.

FIG. 1 d shows a DC linearized circuit model of the PV system of FIG. 1a with DC-DC MICs.

FIG. 2 shows the cost and volume per energy storage for a sample ofdiscrete capacitors and inductors suitable for power applications.

FIG. 3 shows a sampling of tracking and conversion efficiencies reportedin the literature for MPPT algorithms and DC-DC MICs, respectively, aswell as calculated total efficiencies.

FIG. 4 shows a model of a photovoltaic panel.

FIG. 5 shows an plot of the tracking efficiency achieved as the stringcurrent is changed.

FIG. 6 shows a plot of the tracking efficiency versus the number ofpanels used and the maximum conversion ratio used for the DC-DC powerconverter.

FIG. 7 shows an example of a 5-level Marx converter, according to someembodiments.

FIG. 8 shows switching configurations for the 5-level Marx converter invarious phases of operation and for different conversion ratios.

FIG. 9 shows a circuit model for modeling capacitive switching loss.

FIG. 10 shows a circuit model which enables a switching loss evaluationin the Marx converter for active MOSFETs.

FIG. 11 shows an example of a gate drive circuit for a multilevel outputDC-DC switched capacitor converter, according to some embodiments,including a variable resistor for biasing a zener diode.

FIG. 12 shows the predicted performance versus the number of panels usedand the maximum conversion ratio used for the DC-DC power converter.

FIG. 13 shows a plot of converter efficiency versus switching frequencyfor various conversion ratios.

FIG. 14 shows plots of efficiency versus output current.

FIG. 15 shows simulated time domain waveforms for the capacitor currentsand system currents in the Marx converter.

FIG. 16 shows a linearized model of the central input current-controlledinverter.

FIG. 17 shows step responses of the closed-loop transfer functions inequations (22) and (23) used in the linearized model.

DETAILED DESCRIPTION

Implementing per panel MPPT (Maximum Power Point Tracking) at the PVmodule level can facilitate obtaining the maximum amount of power fromeach PV module despite varying light levels, temperatures, panel ages,etc. The improvements can be particularly significant with physicallywidespread solar arrays. With per-panel MPPT, global tracking efficiencycan be significantly improved over simple series or parallel connectionsof PV panels, but the installation of a power converter in each panelcan significantly impact the overall cost of the PV array. Powerconverter lifetimes and replacement costs become even more significantwith per-panel conversion.

A module integrated converter (MIC) is a device that includes a powerconverter configured to obtain power from an individual PV module. Toimplement per panel MPPT, a MIC can be connected to each PV module of asolar array. In addition to having a power converter, each MIC can havea controller that runs a MPPT algorithm to determine the optimaloperating point for the PV module, which may vary in response toconditions such light level, temperatures, panel age, etc. To set theoperating point of the PV module to its maximum power point, thecontroller controls the operating point of the power converter. Forexample, the controller can set the conversion ratio of the powerconverter such that an optimal amount of current flows through the PVmodule to obtain the maximum amount of power from the PV module.

A typical goal of power conversion circuitry associated with a PV systemis to convert DC power extracted from one or more PV modules into ACpower that can be provided to the AC power grid, with high efficiency.To achieve these goals, various approaches can be taken using moduleintegrated converters. Several types of MICs can be used, such as aDC-AC MIC or DC-DC MIC. A DC-AC MIC includes a DC-AC power converterthat converts a DC signal from the PV module to an AC signal which mayultimately be provided to an AC power grid. A DC-DC MIC includes a DC-DCpower converter that converts a first DC voltage and current from the PVmodule into a second DC voltage and current at its output. A centralinverter can be used to convert the DC voltages provided by the DC-DCMICs into AC grid power.

There are advantages of a DC-DC MIC (Module IntegratedConverter)+central DC-AC approach over a DC-AC MIC approach. Theseinclude the availability of a single DC bus for an entire array andintermediate power ripple filtering, as well as added degrees of freedomfor MPPT control.

In some exemplary embodiments of the innovative techniques describedherein, a PV system includes a plurality of PV panels, each having aDC-DC MIC for operating the individual PV panels at their maximum powerpoints. To reduce the cost of such a system, the DC-DC MICs may beimplemented with DC-DC power converters that do not include electrolyticcapacitors or magnetic components. For example, as discussed in furtherdetail below, the DC-DC power converter may be implemented as amultilevel output DC-DC switched capacitor power converter, such as aMarx converter. A central inverter connected to the DC-DC MICs canpresent a substantially constant current source to the DC-DC MICs, whichenables decoupling the local MPPT control from that of other MICs andthe global power tracking controller.

1.1 System Overview

FIG. 1 a shows an example of a PV system 10, according to someembodiments. PV system 10 includes a plurality of PV units PV₁, PV₂, andPV_(N.) As used herein, the term “PV unit” refers to any type ofphotovoltaic element, such as a PV cell, PV module or PV system. Asshown in the embodiment of FIG. 1 a, each of PV units PV₁, PV₂, andPV_(N) can be an individual PV module (also referred to herein as a PVpanel). FIG. 1 b shows an example of a PV module 1 and its conventionalsymbol. PV module 1 may include a plurality of PV cells 2 which may beconnected in series. PV module 1 typically may have a surface area onthe order of about 1 m², and PV cells 2 may be approximately the size ofa semiconductor wafer, e.g., around 6 inches across, for example.However, any suitable size and configuration of PV module/unit unit maybe used, as the techniques described herein are not limited in theserespects.

As shown in FIG. 1 a, each PV unit is connected to the input of anassociated MIC. For example, PV₁ is connected to MIC₁, PV₂ is connectedto MIC₂ and PV_(N) is coupled to MIC_(N). As shown in FIG. 1 a, the MICscan be connected in series with one another such that they share thesame string current I_(string) at their output ports. The term “string,”as used herein, refers to a plurality of circuits connected in seriesand sharing a same string current I_(string). PV system 10 also includesan inverter 3 that converts the DC string current I_(string) into an ACsignal. As shown in FIG. 1 a, the inverter 3 can provide AC voltage tothe power grid at the output of the inverter 3.

As shown in FIG. 1 c, each MIC can include a power converter 4, such asa DC-DC power converter, and a MPPT controller 6 to control the powerconverter. The input port of the power converter can be coupled to theterminals of an associated PV unit. The output port of the powerconverter can be coupled to the output ports of the power converters ofother MICs in a series combination, as shown in FIG. 1 a. However, thetechniques described herein are not limited to a series combination ofMICs, as the MICs could be connected in parallel, in a combination ofseries and parallel, or in another configuration. For purposes ofillustrating the techniques described herein, the series combination ofMICs shown in FIG. 1 a will be discussed by way of example.

In some embodiments, the power converter 4 may be implemented as amultilevel output DC-DC switched capacitor power converter, such as aMarx converter, for example. Such a converter can convert an input DClevel into an output DC level using a selected conversion ratio from aset of conversion ratios that can be implemented by the converter (e.g.,from 0 to a maximum integer value). Advantageously, using a multileveloutput DC-DC switched capacitor power converter as the power converter 4may provide a low component-cost power converter with a long lifespan.By contrast, conventional DC-DC converters often use magneticcomponents, such as inductors or transformers, as energy storageelements. However, the component cost of magnetic components can beprohitive. In some embodiments, power converter 4 may not include anymagnetic components such as inductors or transformers (though parasiticinductances may be present). An exemplary multilevel output DC-DCswitched capacitor power converter and the operation thereof will bediscussed further below with reference to FIGS. 7 and 8.

MPPT controller 6 may be implemented using any suitable microprocessoror using dedicated hardware, for example. MPPT controller 6 can executeinstructions to control the power converter 4 to extract power from theassociated PV unit at approximately its maximum power point. Forexample, the MPPT controller can control the conversion ratio of thepower converter 4 so that the current and/or voltage produced at theterminals of the PV unit will result in maximum power extraction fromthe PV unit. The MPPT controller 6 may execute a perturb-and-observealgorithm or other MPPT algorithm such as those known in the art.However, any suitable MPPT algorithm may be used, as the techniquesdescribed herein are not limited to a particular MPPT algorithm.

In the PV system of FIG. 1 a, the inverter 3 can control the stringcurrent I_(string). For example, the inverter 3 can include a controller7 that executes instructions to control the inverter 3 to establish aparticular string current I_(string). Alternatively, the controller 7can be separate from the inverter 3. In some embodiments, the stringcurrent can be controlled by controller 7 to be substantially constant.Advantageously, by providing a substantially constant string current,the MPPT algorithms run by the individual MICs can be decoupled from oneanother, as the current through the string of MICs is, at leasttemporarily, independent of the operating parameters of any particularPV unit. Thus, each MIC can optimize the power extracted from its PVunit without being affected by the varying electrical characteristics ofthe other MICs in the string as they attempt to maximize their MPP.

To find the global maximum power point, the controller 7 can graduallychange the string current to different values across a range of currentvalues. For each string current value, the MICs can determine themaximum power points of the individual PV units. In some embodiments,the rate at which the MICs change their operating parameters in responseto the MPPT algorithm run by MPPT controller 6 can be much faster thanthe rate at which controller 7 changes the string current to differentvalues. Thus, due to the difference in control speed, even if controller7 continuously changes the string current, the string current willappear to be substantially constant to the individual MICs, due to themuch higher rate at which the MICs can change the operating parametersof the PV panels. As the string current is changed through a range ofvalues, the controller 7 can save an indication of the total amount ofpower produced at different string currents (e.g, see FIG. 5). Aftersweeping through a range of options, the controller 7 can determinewhich string current resulted in the highest total power production. Thecontroller 7 can then select this optimal string current and controlinverter 3 such that the optimal string current flows through theinverter 3. Such a procedure may be repeated at various intervals tore-optimize the string current.

Although a technique has been described for tracking the global MPP bysweeping through various string currents, any suitable algorithm may beused by controller 7 for tracking the global MPP, as the techniquesdescribed herein are not limited to the use of a particular algorithmfor tracking the global MPP.

Advantageously, the control implemented within the MICs and controller 7can be performed autonomously by each device. No communication is neededbetween the MICs or the controller 7, which can reduce the cost ofproviding communication lines or a communication network between theMICs and controller 7. However, communication between the MICs and/orthe controller 7 may be provided, if desired for a particularimplementation.

The system level approach is further illustrated by the DC linearizedcircuit model with an N-panel PV string with DC-DC MICs, as shown inFIG. 1 d. Ideal transformers can be used to model the function of DC-DCMICs, with the integer number of turns on the secondary, Q_(i),representing the conversion ratio of the DC-DC MIC when implemented as amultilevel output DC-DC switched capacitor converter. The DC-DC moduleconversion ratios are selectable, but discrete. The conversion ratioQ_(i) is the ratio between the input voltage of the DC-DC powerconverter and its output voltage. Due to the finite number of discreteconversion ratios Q_(i), the output of the converter will have one of aset of levels for a given input, depending on the conversion ratiochosen.

As discussed above, the responsibility of MPPT is shared among the DC-DCMICS and the central inverter. As a result, the required complexity ofthe DC-DC MICs is simplified. A central ripple-port inverter can be usedas inverter 3 to reduce the AC ripple that reaches the MICs. Per panelmagnetics can be eliminated as well as electrolytic capacitors. Anymagnetics that are used for the ripple port inverter need only bepurchased once per string.

As used herein, the term “ground” and its associated symbol(s) can referto various reference voltages such as a local panel “ground” or afloating ground reference. For example, when connected in a seriesstring, each PV panel and MIC can be referenced to a differentpotential. Thus, as used herein, the term “ground” and its associatedsymbol(s) do not necessarily refer to earth ground, i.e., the potentialof the earth. Rather, the term “ground” and its associated symbol(s)herein refer to a voltage reference which may be constant in some cases.However, in some embodiments particular circuits may be referenced toearth ground depending on their configuration.

1.2 Switched Capacitor Benefits

Switched capacitor converters achieve current and voltage conversionwithout magnetic energy storage (aside from that inherent in parasiticinductances present in wires of any length). FIG. 2 shows the cost andvolume per energy storage (μJ) for a sample of discrete capacitors andinductors suitable for power applications, including discrete inductors(10 μH-1 mH/100 mA-1 A) and capacitors (Ceramic and Film 1-10 μF/10-100V) sampled from a commercial catalog. Energy storage was calculated as½CV² or ½LI² for maximum rated voltages and currents. These data implya-priori expected cost and volume benefits of switched capacitorconverters when compared to inductor-based converters.

1.3 Total Efficiency

Total efficiency is an important parameter in the design and evaluationof PV systems. Here we define total efficiency, η, as the product oftracking efficiency, η_(p), and conversion efficiency, η_(c):

η=η_(p)×η_(c).  (1)

Tracking efficiency can be defined as the power produced at theoperating point of the PV unit divided by the power that would beproduced at the PV unit's maximum power point. Conversion efficiency canbe defined as the power provided at the output of the power electronicsdivided by the power produced by the PV units at the input of the powerelectronics. FIG. 3 depicts a sampling of tracking and conversionefficiencies reported in the literature for MPPT algorithms and DC-DCMICs, respectively. The two ranges of efficiencies can be multipliedyielding a third range corresponding to total efficiency, η, as shown inFIG. 3.

2 MAXIMUM POWER POINT TRACKING

Maximum power point tracking in the system of FIG. 1 a is simplified bythe input current control of the central inverter 3 and the seriesconnection of the MICs. The selectable conversion ratios, Q_(i), allowthe DC-DC MICs to track local MPP's as the string current slowly varies.The central inverter can track the global MPP by adjusting its inputcurrent.

The run-time global MPPT can be implemented by exploiting time-scaleseparation. As discussed above, the local MPPT control at the MICs canoperate relatively quickly, and the global MPPT control can operaterelatively slowly. Specifically, on the time-scale of local MPPTcontrol, the string current, I_(o), may be taken to be static or“quasi-static.” Because the maximum power point of each panel is definedby a unique maximum power current, I_(mp,i), the quasi-static stringcurrent naturally decouples MPPT control among the modules.

2.1 PV Model

FIG. 4 shows a model of the photovoltaic panel and its parameters. Giventhe parameters quoted in a typical datasheet, V_(oc), I_(sc), and themaximum power voltage and current, V_(mp), and I_(mp), analysis of thecircuit in FIG. 4 yields

$\begin{matrix}{V_{dp} = V_{oc}} & (2) \\{R_{s} = \frac{V_{oc} - V_{m\; p}}{I_{m\; p}}} & (3) \\{R_{p} = \frac{{I_{sc}R_{s}} - V_{oc}}{I_{m\; p} - I_{sc}}} & (4) \\{{I_{p\; h} = {I_{m\; p} + \frac{V_{fwd}}{R_{p}}}},} & (5)\end{matrix}$

where V_(dp) is the forward voltage of the diode, D_(p), in the model.In FIG. 4, when I_(in)<I_(mp), the diode, D_(p), is forward-biased andit is reverse-biased otherwise. The resulting panel voltages are

V _(in) =V _(dp) −I _(in) R _(s) ,I _(in) <I _(mp)

V _(in) =R _(p) I _(ph)−(R _(s) +R _(p))I _(in) ,I _(in) ≧I ^(mp)  (6)

and the panel power is simply

P _(in) =I _(in) V _(in)  (7)

The following nominal datasheet values were adapted from a MITSUBISHIPV-MF170EB4:

I _(mp)=6.93A

V _(mp)=24.6V

I _(sc)=7.38A

V _(oc)=29V  (8)

2.2 Local Maximum Power Point Tracking

Local MPPT control can be performed by matching the string current tothe panel's own I_(mp,i)'s. From FIG. 1 d, the i^(th) panel current is

I _(in,i) =Q _(i) I _(o).  (9)

Given a quasi-static string current, I_(o), the modules each choose aQ_(i) to maximize their panel power. This maximization step can beperformed a number of ways. For instance, the modules may estimate theirI_(mp,i)'s via short-circuit current measurements. A perturb and observestep may be used to provide good accuracy following the initial I_(mp)guess.

In the simulations that follow, the local algorithm for choosingconversion ratios was implemented as follows. Given I_(mp,i) either bythe short-circuit method described above or otherwise, the modulesattempt to minimize the error |I_(in,i)−I_(mp,i)|. This minimization isconstrained according to the nonlinear behavior of the PV indicated inFIG. 4. Combining equations (6) and (7), the panel power for the i^(th)panel can be written:

P _(in,i) =I _(in,i) V _(dp,i) −I _(in,i) ² R _(s,i) ,I _(in,i) <I_(mp,i)

P _(in,i) =I _(in,i) R _(p,i) I _(ph,i)−(R _(s,i) +R _(p,i))I _(in,i) ²,I _(in,i) ≧I _(mp,i).  (10)

Taking the derivative of (10) with respect to I_(in) yields

$\begin{matrix}{{{\frac{\partial P_{{i\; n},i}}{\partial I_{{i\; n},i}} = {V_{{dp},i} - {2I_{\; {{i\; n},i}}R_{s,i}}}},{I_{{i\; n},i} < I_{{m\; p},i}}}{{\frac{\partial P_{{i\; n},i}}{\partial I_{{i\; n},i}} = {{R_{p,i}I_{{p\; h},i}} - {2\left( {R_{s,i} + R_{p,i}} \right)I_{{i\; n},i}}}},{I_{{i\; n},i} \geq {I_{{m\; p},i}.}}}} & (11)\end{matrix}$

The term, −2(R_(s,i)+R_(p,i))I_(in,i), in the derivative typically leadsto a steep decrease in panel power for I_(in)≧I_(mp). Absolute errors|I_(in,i)−I_(mp,i)| impact the panel power less for I_(in,i)<I_(mp,i).Accordingly, a suitable algorithm can attempts to minimize the error|I_(in,i)−I_(mp,i)| with the following order of preference:

-   -   1. I_(in,i)=I_(mp,i)    -   2. I_(in,i)<I_(mp,i)    -   3. I_(in,i)>I_(mp,i)

In the examples presented here, the DC-DC modules each continuouslyattempt to match the string current to their own MP currents accordingto the above algorithm. Generally, the MICs can choose from a set ofintegral conversion ratios [0,1 . . . Q_(max)]. The Q=0 moduleconfiguration can assist in providing good average tracking efficiency.It represents the option for a panel to “sit out” when its maximum poweris so low that including it in the string would have a negative impacton the global MPP.

2.3 Global Maximum Power Point Tracking As discussed above, the stringinverter 3 can track the global MPP by adjusting its input current. FIG.5 depicts an example of the tracking efficiency achieved as I_(o) isswept, while the DC-DC modules adjust their conversion ratios. FIG. 5shows a single I_(o) sweep in a simulated system with 3 panels,Q_(avail)=[0, 1, 2, 3, 4], I_(mp,vec)=[6.898, 4.503, 4.878] A, andΔI_(o)=1 mA. For this example, and for the rest of this section,tracking efficiency is considered in an otherwise lossless system(η_(c)=100%). Section 4 addresses the effect of converter efficiency onMPPT control.

The I_(o) sweeps, like the one depicted in FIG. 5, may be performed on ascheduled basis. Alternatively, I_(o) may be varied continuouslyaccording to a particular runtime MPPT algorithm. Section 4.5 presents asimulation of an example of an input current-controlled inverter.

2.4 Statistical Performance Evaluation

A statistical performance evaluation method was adopted to account forvariations in panel MPP's. Monte Carlo simulations were performed byselecting random (normalized) I_(mp,i)'s for each panel. For eachsimulation, the string current, I_(o), was swept as in FIG. 5 and themaximum efficiencies (tracking, converter, and total) were recorded.Repeating this many times and averaging the results yielded a predictionof average performance. An example output plot is shown in FIG. 6 forQ_(avail)=[0:1:Q_(max)], Monte Carlo Length=200,I_(o,sweep)=[0.01:0.02:6.93] A.

The plot in FIG. 6 shows that tracking efficiency can be very high foronly a few panels. As panels are added, η_(p) diminishes to a limitedextent. The local MPPT algorithm implemented impacts this behaviorsignificantly. For instance, if the order of preferences listed inSection 2.2 is reversed, the tracking efficiency diminishes steadily aspanels are added rather than flattening as it does in FIG. 6. The MonteCarlo simulation results also show how average tracking efficiencyimproves as the number of available levels increases. The trackingefficiency predicted for a 3-panel, 5-level system is approximately 90%.Increasing the number of available levels to 8 increases the predictedtracking efficiency to 95%, in this simulation. Thus, in someembodiments, a multilevel output DC-DC switched capacitor capacitorpower converter for a PV unit may be capable of selecting from arelatively small number of conversion ratios such as no more than five,no more than eight, or no more than ten conversion ratios, for example,which can simplify the converter circuit and operation. However, thetechniques described herein are not limited as to converters with a lownumber of possible conversion ratios, as converters with larger numbersof conversion ratios may be used, in some implementations. Finally, itshould be noted that the Q_(max)=1 case (i.e. Q_(avail)=[0,1]) issomewhat representative of a simple series string of panels with bypassdiodes. The statistical data predict roughly 65% average trackingefficiency while a 5-level MIC would improve that efficiency to roughly90%, in these simulations.

2.5 Effect of Spatial Panel Separation

In the above example, the panels are assumed to have a random anduncorrelated distribution of MPP's. This model becomes less appropriateas panels become closely spaced. To model the effect of statisticalcorrelation between MPP's for panels arranged in a non-infinite area,the randomly assigned panel MPP's can be constrained to a fraction ofthe full range. The simulation above was repeated having forced theMPP's to lie within 50% of the full range for each Monte Carloiteration. The results show universally higher average trackingefficiencies. For instance, the tracking efficiency predicted for a3-panel, 5-level system is approximately 95.5% and for a 3-panel,8-level system, 97.4%.

2.6 Non-Integral Level Selections

As described herein with respect to the Marx converter, switchedcapacitor multilevel converters can have integral, boosting sets ofconversion ratios. In a boosting switched capacitor multilevelconverter, the input voltage is multiplied by approximately the integralconversion ratio to determine the output voltage of the converter. Whenthe conversion ratios Q are limited to a fixed number of integer values,the output of the converter is limited to a fixed number of discretelevels for a given input. However, other switched capacitor topologiescan be used that achieve rational or bucking conversion ratios. When abucking converter is used, the input voltage can be divided by anintegral conversion ratio to determine the output voltage. A combinationof a bucking and boosting topology may be used to achieve rationalconversion ratios (e.g., 2/3, 4/3, etc.) rather than integral conversionratios (e.g., 1, 2, 3). Such topology choices may be beneficial whenconsidering upper bounds on DC bus voltages or other practical issues.

3 SWITCHED CAPACITOR IMPLEMENTATION

FIG. 7 shows a particular embodiment of the switched capacitor MICs inFIG. 1 d: the Marx multilevel converter. By forming series and parallelcombinations of the input source and the switched capacitors, the5-level Marx converter shown in FIG. 7 can achieve conversion ratiosQ_(avail)=[0, 1, 2, 3, 4]. Exemplary switching patterns for achievingthese conversion ratios are discussed in the following section.

As shown in FIG. 7, a power diode 8 can be coupled at the output of theMarx converter to limit the direction of current flow. Power diode 8will be discussed in further detail below. An output capacitor 9 can beconnected between the output terminal of the diode and ground to smoothvariations in the output voltage of the Marx converter. The output ofthe Marx converter can be taken across the output capacitor 9.

3.1 Efficient Switching Patterns

Switching cycles include a recharge phase, φ₁, and an output phase, φ₂.During φ₁, the switched capacitors are disconnected from the load andcharged in parallel with the source. During φ₂, one of severalseries-parallel configurations of the switched capacitors and inputsource is chosen to achieve the desired conversion ratio. A Marxconverter may switch between any one or more of the switchingconfigurations shown herein. However, many other switchingconfigurations can be implemented, including redundant configurations.

The switching configurations shown in FIG. 8 were chosen for the 5-levelMarx converter to minimize the conduction losses that will be quantifiedshortly. FIG. 8( a-f) show switching configurations in the rechargephase (FIG. 8 a) and for the five conversion ratios. In FIG. 8, agrayed-out transistor indicates that the transistor is turned off, and atransistor shown in black indicates that the transistor is turned on.Generally, the exemplary switching configurations were chosen tominimize capacitor droop and the number of switches in the outputcurrent path, both of which lead to loss and load regulation. Capacitordroop can be minimized by 1) utilizing the input source to drive theoutput during φ₂ when possible and 2) utilizing all of the switchedcapacitors when driving the output, e.g. parallel-connect redundantcapacitors when possible.

Switched capacitor circuits can achieve very high conversion efficiencyby minimizing the instantaneous current flow through their effectiveoutput resistance, R_(out,i). In a DC-DC switched capacitor circuit, theoutput is slowly-varying on the time-scale of one switching period.These facts guide us to particular modes of operation. In particular,efficient operation can be achieved when the same output phase (φ₂)configuration is repeated every cycle. In contrast, modulation of the φ₂configuration on a per cycle basis, e.g. to achieve intermediateconversion ratios, may lead to continuously varying open circuitconverter voltages resulting in high instantaneous currents (high AC rmscurrents) through R_(out,i). We have found that the Marx multilevelconverter can efficiently achieve a discrete set of conversion ratios.

3.2 Linear Modeling

A linear modeling approach yielded quantitative support for the linearcircuit models shown in FIG. 1 d including the output resistances,R_(out,i) which represent both loss and load regulation in the switchedcapacitor circuits.

3.3 Switching Speed Limit Definitions

Loss and load regulation mechanisms can be differentiated among twoswitching speed limiting cases. In the slow-switching-limit (SSL), theswitched capacitors fully equilibrate, yielding impulsive capacitorcurrents. In the fast-switching-limit (FSL), the switched capacitorsmaintain fixed voltages while capacitor currents during each switchingstate are constant.

The two switching speed limits can be understood by considering theclassic capacitor charging loss problem depicted in FIG. 9. The totalenergy lost in charging the capacitor is the time-integral of I_(c) (t)²R:

$\begin{matrix}{E_{tot} = {{{- \frac{\left( {V_{s} - {V_{C}(0)}} \right)^{2}}{2R}}{{RC}\left( ^{{- 2}\; {t/{RC}}} \right)}}|_{0}^{t}.}} & (12)\end{matrix}$

In the SSL, the exponential term is allowed to collapse to −1 and theenergy lost becomes

E _(tot,SSL)=½CΔV _(C) ²,  (13)

independent of R, and in agreement with the classical result. In theFSL, (12) can be viewed near t=0 with the Taylor series approximation tothe exponential term. This leads to

$\begin{matrix}{{{E_{{tot},{FSL}}(t)} = \frac{\left( {V_{s} - {V_{C}(0)}} \right)^{2}t}{R}},} & (14)\end{matrix}$

i.e. the loss we would expect for two fixed voltages connected acrossthe resistor. These two loss mechanisms yield asymptotic limits to theoutput resistance with proportionalities as follows:

$\begin{matrix}{{R_{SSL} \propto \frac{1}{{Cf}_{sw}}}{R_{FSL} \propto {R_{{ds},{on}}.}}} & (15)\end{matrix}$

The method developed in the paper M. Seeman and S. Sanders, “Analysisand optimization of switched-capacitor dc-dc converters,” PowerElectronics, IEEE Transactions on, vol. 23, no. 2, pp. 841-851, March2008 for computing the multipliers to quantify R_(SSL) and R_(FSL) wasadapted to the Marx multilevel converter here. The results aresummarized in Tables 1 and 2 for Marx converters having between two andeight available levels. Note that the multipliers in the tables need tobe computed for each conversion ratio (switching pattern) for eachnumber of available levels (topology). Also note that R_(FSL) depends onthe duty ratio between φ₁ and φ₂, which was taken as D=0.5 for allswitching patterns here. Given the asymptotic limits, the actual outputresistance for any combination of topology, C, f_(sw), and R_(ds,on) isgenerally

R _(out)=max(R _(FSL) ,R _(SSL))  (16)

and the conduction loss per module is

P _(rloss) =I _(o) ² R _(out).  (17)

TABLE 1 R_(SSL) Multipliers: (×1/Cf_(sw)) Levels Available: 2 3 4 5 6 78 Q = 0 0 0 0 0 0 0 0 Q = 1 0 0 0 0 0 0 0 Q = 2 — 1 1/2 1/3 1/4 1/5 1 Q= 3 — — 2 3/2 1 5/6 2/3 Q = 4 — — — 3 5/2 2 3/2 Q = 5 — — — — 4 7/2 3 Q= 6 — — — — — 5 9/2 Q = 7 — — — — — — 6

TABLE 2 R_(FSL) Multipliers: (×R_(ds,on)) Levels Available: 2 3 4 5 6 78 Q = 0 2 4 6 8 10 12 14 Q = 1 2 4 6 8 10 12 14 Q = 2 — 8 10 12.4 8.217.6 32.4 Q = 3 — — 26 24 38 48.4 50.8 Q = 4 — — — 64 90 100 100 Q = 5 —— — — 130 180 206 Q = 6 — — — — — 232 307 Q = 7 — — — — — — 378

3.4 Switching Loss

The linearized model above captures loss due to output currentconduction. When evaluating the design in Section 4, it can also beuseful to include switching loss, a loss mechanism not explicitlycontained in the linearized circuit model of FIG. 1 d. The switchingloss for any active switch (one that changes state between the twoswitching phases) can be quantified by considering the circuit shown inFIG. 10, which enables a switching loss evaluation in the Marx converterfor active MOSFETs

All MOSFETs in the Marx converter reside in at least one loop includingonly one or two other MOSFETs and a switched capacitor. In the Marxconverter, the switched capacitor, C, in FIG. 10 will nominally exhibita voltage equal to the panel voltage, V_(in), because it is recharged tothat potential each cycle. The total switching loss was estimated interms of typical data sheet values using for N active devices as

P _(swloss) =N(Q _(g) V _(g)+½Q _(loss) |V _(in) |+Q _(rr) |V _(in)|)f_(sw).  (18)

Examining the switching patterns shown in FIG. 8, one can extract thefollowing pattern generalizing the number of active switches accordingto conversion ratio:

N=1,Q=0

N=3Q−2,Q>0.  (19)

3.5 Additional Features

The topology of the Marx converter can provide several advantageousfeatures that may add significant value to a solar power system. Asmentioned previously, the Marx converter has a natural pass-throughfeature, which can replicate the function of bypass diodes. Whenswitched into the Q=0 mode in which the conversion ratio is zero, asshown in FIG. 8( b), the output of the Marx converter is connected topanel ground. As a result, the ouptut of the converter is shorted, whichallows the converter to appear as a short within the string.Advantageously, by using the Marx converter in the Q=0 mode, the bypassfeature can be implemented through control of the Marx converter itself,without the need to add additional switches or bypass diodes separatefrom the converter.

Another advantage of the Marx converter is the ability to disconnecteach module from the load. Such a feature can be beneficial whenimplementing a safety disconnect feature. Conventionally, a problem canarise in the case of a fire because the series-connected string of PVmodules can create a voltage that is hazardous to firefighters. Oneconventional technique for preventing hazardous voltages is for thefirefighters to cover the PV panels with a dropcloth that prevents lightfrom reaching the panels.

An improved solution to avoid electrocution hazards may be realizedusing the Marx converter. For example, there may be a need for adisconnect in the event of a fire to prevent electrocution hazards thatwould otherwise result from the high voltage string output. When a fireoccurs, a safety disconnect feature can be implemented by setting theMarx converters for each PV unit into the recharge state illustrated inFIG. 8 a, whereby each PV unit is decoupled from the output of itsassociated Marx converter. By isolating the PV units from the outputs ofthe MICs, the situation can be prevented whereby relatively low PV unitvoltages are combined in series to produce a hazardous voltage. A PVinstallation can be provided with a conspicuously-located button thatcan be pressed by a firefighter or other individual to implement thesafety disconnect feature. A signal can then be sent to each of the MICsto set the Marx converters into a safety configuration (such as thatshown in FIG. 8 a). Alternatively, the safety feature may beautomatically activated in response to activation of a fire alarm.

Such a disconnect feature may also be particularly beneficial inimplementing an anti-islanding mode.

Another advantage is that the run-time local MPPT algorithm describedabove can be designed to automatically prevent under-voltage conditionsat the panel output. In conventional power converters, an under-voltagecondition can cause the power converter and/or its associated gate drivecircuit to malfunction. Such a condition can be avoided using thetechniques described herein. Because the DC-DC modules continuouslychoose Q_(i) to closely match I_(in,i) to I_(mp,i), they automaticallyadjust to over-current conditions, choosing Q_(i)=0 in the limitingcase. This feature may be advantageous when the local control circuitryis powered by the panel itself.

3.6 Gate Drive

The gate drive circuit for the Marx converter may operate with acontinuous floating gate drive voltage, as the converter itself does notguarantee a periodic charging path to recharge a bootstrap capacitor. Anembodiment of a gate drive circuit is shown in FIG. 11 a. The transistorof the Marx converter to be driven by the gate drive circuit is shown inFIG. 11 a as transistor M.

A level shift circuit 15 can translate ground-referenced logic signalsto the gate drive output. The level shift circuit 15 can be implementedas a commercial high side driver IC such as the IR2125. However, thehigh voltage rating of such a part may be under-utilized for a typicalimplementation of the system in this work. Therefore, a morecost-effective gate drive may include a custom level shift circuit.However, any suitable level shift circuit may be used. In the embodimentof FIG. 11 a, the level shift circuit 15 may receive suitable power andground signals, such as panel-referenced power and ground signals. Alogic signal can be received at the input IN which can be provided by acontroller that controls the timing at which the transistor M is to beswitched. A bootstrap capacitor 25 can be provided between terminals Vsand VB that is charged to a suitable voltage for driving the gate oftransistor M. When the transistor is to be turned on, the terminals VBand HO of the level shift circuit 15 can be connected internally,thereby applying the capacitor voltage to the gate of transistor M viathe terminal HO and an optional gate resistor Rg.

In this embodiment, the 555 timer IC 16, diodes 17, 18, and floatingcapacitor 21 act as a charge pump circuit to generate a suitable voltagefor bootstrap capacitor 25. Although a timer 555 circuit IC described inthis embodiment, any suitable timer circuit or any suitable oscillatormay be used. Capacitor 26 and resistor 27 can have suitable values forsetting the timing of the 555 circuit. A zener diode 20 and filtercapacitor 28 can provide a voltage source (e.g., at 15 V) connected tothe power terminal of the timer circuit 16. When the output OUT of thetimer circuit 16 is low, the floating capacitor 21 is charged. In thisexample, floating capacitor 21 is charged to 15 V. When the output OUTof the timer circuit 16 goes high, the voltage of the low-side terminalof floating capacitor 21 is increased (e.g., to 15 V), which causes thevoltage of the high-side terminal of the floating capacitor 21 to beincreased by the same amount (e.g., to 30 V). The 30 V signal is thentransferred to the bootstrap capacitor 25 via diode 17. When terminal VSis at 15 V, the charge pump circuit thereby can charge the bootstrapcapacitor 25 to 15 V referenced to VS. In this example, the charge pumpdrives the VB node to twice its supply voltage referenced to its ownfloating GND leading to a 15 V floating drive referenced to the MOSFETsource. This voltage can be adjusted by choosing the voltage of theZener diode.

The resistor 19 between the 555 timer GND terminal and Panel GNDterminal and the zener diode 20 allows the ground pin of timer IC 16 tofloat 15 V below the source of the driven MOSFET M. The low powerversion of the 555 timer IC (ICM755) can be used in this circuit toachieve low power dissipation in the part itself and to achievesufficient quiescent current despite the resistor 19 to ground. Theresistance of resistor 19 can be selected based on which transistor ofthe converter is being driven (and its corresponding source voltage)and/or based on the conversion ratio being implemented by the powerconverter. In some embodiments, resistor 19 can be implemented as avariable resistor. Implementing resistor 19 as a variable resistor canenable setting the current through the zener diode 20. The currentthrough the zener diode 20 can be chosen to be just high enough so thatthe zener diode is appropriately biased. Higher current through thezener diode may result in unneeded loss and therefore reducedefficiency. The resistance of resistor 19 can be selected to set thecurrent through the zener diode 20 in view of these considerations. Whenthe source voltage of the transistor M varies over time, the timeaverage source voltage may be used when determining a suitableresistance value. Any suitable type of variable resistor may be used.

FIG. 11 b shows an example of a variable resistor 19, according to someembodiments. As shown in FIG. 11 b, variable resistor 19 includesseveral resistors R of different resistances connected in parallel, witheach resistor being in series with a switch S. One or more switches Scan be turned on to select a suitable resistance value. If the switch isconnected with its source to ground and drain to the resistor and it isan N-type gransistor, in may be controlled with a ground-referencedsignal directly, e.g, from the ouptut pin of a microcontroller alreadyincluded in the controller 6.

In some embodiments, a gate drive circuit for a Marx converter caninclude several of the circuits of FIG. 11 for each high-side transistorhaving a source that is not referenced to ground. Different gate drivevoltages can be generated for different transistors of the Marxconverter, as needed.

4 DESIGN EXAMPLE

A 3-panel 510 W system was designed and simulated in SPICE and inMATLAB. Among the key topological considerations for implementing apractical Marx DC-DC MIC is the option of using a power diode in serieswith the output of each module. Such a diode can be used to blockcurrent from conducting backwards through the body diode of the upperMOSFET in the output stage during φ₁. In order to alleviate any need tosynchronize switching action among modules, a local outputnon-electrolytic capacitor can be placed across each MIC to create alocal DC bus.

4.1 Number of Levels

The number of conversion levels of the multilevel converter was chosenusing the same Monte Carlo prediction methods described in Section 2.4.Having enumerated loss mechanisms, total efficiency was used todetermine performance. To choose an appropriate number of conversionlevels, an unoptimized but lossy system was simulated using nominalcircuit parameters and MOSFET device characteristics. The predictedperformance is plotted in FIG. 12 for a system with the followingparameters: Q_(avail)=[0:1:Q_(max)], Monte Carlo Length=400,I_(o,sweep)=[0.01:0.02:6.93] A, C=12.5 μF, f_(sw)=250 kHz, R_(dson)=10mΩ, Q_(g)=10 nC, Q_(oss)=5 nC, Q_(rr)=25 nC, V_(g)=15 V, V_(oc)=29 V,V_(mp)=24.6 V, I_(sc)=7.38 A, I_(p)=6.93 A, Distribution Compression=50.The data show diminishing returns in total efficiency beyond 5 levels.Therefore a 5-level Marx converter may be chosen for the MIC. However, aconverter with any suitable number of levels may be chosen depending onthe application.

4.2 MOSFET Choice and Switching Frequency Optimization

Having chosen a suitable value for the non-electrolytic (e.g., metalfilm) switched capacitors in the 5-level Marx converter, the choice ofMOSFET and switching frequency can be optimized together. All MOSFETs inthe Marx converter may reside in loops containing a switched capacitorand other MOSFETs only. MOSFET drain-source voltages can therefore beupper bound by the maximum panel voltage. Accordingly, it can beadvantageous to choose a panel whose open-circuit voltage is just belowa standard value for V_(dss). Over-sizing the MOSFET beyond the requiredV_(ds) rating may lead to unneeded switching or conduction loss and asuboptimal design. A number of likely MOSFETs can be identified havingV_(dss)=30 V for the panel open-circuit voltage of 29 V. SuitableMOSFETs can be chosen based on their on-resistance, R_(ds,on), and gatecapacitance, C_(g). With the losses derived in (17) and (18), theperformance was plotted for each MOSFET across switching frequency andconversion ratios. FIG. 13 shows such a plot for the selected MOSFET(IRF8721, C=12.5 μF, V_(mp)=24.6 V, I_(mp)=6.93 A, MP=170 W, V_(g)=10V). A maximum average converter efficiency (across all conversionratios) of >98% was predicted at a switching frequency of 360 kHz. Notethat the gate drive voltage was decreased from 15 V in the unoptimizedsystem to 10 V in the optimized system. Adjusting the gate drive voltagetrades off conduction loss (on-resistance) for switching loss.

Any suitable switching frequency may be used in the DC-DC powerconverter. In some embodiments, a switching frequency of between 10 kHzand 500 kHz, inclusive, may be chosen, based on the considerationsdiscussed herein, such as minimizing losses.

4.3 Power Diode

The power diode 8 can be chosen to support the peak output current andto block the peak reverse voltage safely. Secondly, it can be chosen forlow capacitance, forward voltage, and ESR. Having added output diodes tothe implemented system, the additional losses can be estimated asfollows:

$\begin{matrix}{V_{{fwd},i} = {{{\ln \left( \frac{I_{o}}{I_{s} + 1} \right)}n\frac{kT}{q}} + {{ESR}_{diode}I_{o}}}} & (20) \\{{P_{diode} = {{I_{o}{\sum\limits_{i}\; V_{{fwd},i}}} + {f_{sw}C_{j,i}V_{{rr},i}^{2}}}},} & (21)\end{matrix}$

where V_(rr) is the reverse voltage during φ₁ and C_(j) is the junctioncapacitance of the diode. This expression can be used to improve theaccuracy of the Monte Carlo performance predictions. An example of asuitable power diode is Motorola MBR20100C Shottky diode. However, anysuitable power diode can be used.

4.4 Simulated Prototype

The optimized system was simulated using SPICE and MATLAB. Theperformance of this system was predicted with Monte Carlo methods havingincorporated the losses derived in (17), (18) and (21). The results areshown in Table 3 for the following parameters: 5-level converter, 3Panel optimized system: Monte Carlo Length=100, DistributionCompression=50%, ΔI_(o)=1 mA, Diode Loss=[on].

TABLE 3 Simulated statistical performance: simulated efficiency symbolresult tracking η_(p) 95.43% conversion η_(c) 97.56% total η 93.10%

A summary of circuit elements selected for the simulated prototype isshown in Table 4.

TABLE 4 Circuit component summary Part Component No./Value Note Switched12.5 μF Metal Film Capacitors, Output 1P4.7P6.8 μF Capacitor Panel   25μF 12.5P12.5 μF Capacitor MOSFET IRF8721 Output Diode MBR20100C

The central inverter may not track panel power, corresponding to η_(p),directly. Instead it tracks its input power, corresponding to η. Havingincorporated the loss mechanisms from Section 3 and in equation (21),this observation was accounted for in simulation by allowing theinverter to choose the I_(o) that maximized its input power. Trackingefficiency was recorded for comparison to total efficiency.

An experiment was performed in simulation to validate the linearmodeling effort and loss calculations above. A fixed set of conversionratios and MPPs was chosen for the three panels. Tracking, conversion,and total efficiencies were plotted for a single I_(o) sweep. FIG. 14compares the results for calculated data based on Section 3 and equation(21), a SPICE simulation of the linearized model and a SPICE simulationof the MOSFET system. The difference in η_(c) between the linearizedmodel and the other two data sets represents switching and output diodeloss. Errors between the calculated model and FET simulation are likelydue to estimation errors in computing diode and switching losses. Notethat in the plots of FIG. 14, the maximum in total efficiency lines upclosely with the maximum in tracking efficiency. The parametersassociated with the plots of FIG. 14 were a Single I_(o) sweep, 3sources, Q=[0, 2, 4], I_(mp,vec)=[0.007 3.465 6.93] A, C=12.5 μF,f_(sw)=360 kHz, MOSFET: IRF8721, V_(g)=10 V, deadtime=100 ns, R_(g)=4 Ω.

Time domain waveforms from the simulated system are shown in FIG. 15.FIG. 14 shows a zoom-in of the capacitor currents. The shape of thosecurrents indicates operation between the slow and fast switching limitsdefined in Section 3.3. This result is a natural outcome of the MOSFETchoice and switching frequency optimization step above.

FIG. 14 shows panel input currents during a step change in the loadcurrent from 90% to 100% of the predicted maximum power current. In thisexample, Panel 1 is bypassed (Q₁=0) because its MPP is quite low;I_(in1)=0 in the plots. The other two panels initially settle close totheir respective I_(mp,i)'s-Panel 2 exhibits half of the photovoltaiccurrent that Panel 3 does. When the load current steps to its maximumpower value, I_(in2) and I_(in3) settle on their respective I_(mp,i)'s.

4.5 DC AC Dynamics

A linearized model of the central input current-controlled inverter isshown in FIG. 16. The closed-loop transfer functions of particularinterest can be derived from that circuit. They are

$\begin{matrix}{{\frac{{\hat{i}}_{i\; n}}{{\hat{v}}_{i\; n}}(s)} = {\frac{M^{2}(D)}{{sL}_{e} + R_{e} + {{RP}\frac{1}{sC}}}\left( \frac{1}{1 + {T(s)}} \right)}} & (22) \\{{{\frac{{\hat{i}}_{i\; n}}{{\hat{v}}_{ref}}(s)} = \frac{A(s)}{1 + {{A(s)}{F(s)}}}},} & (23)\end{matrix}$

where

$\begin{matrix}{{A(s)} = {{G_{c}(s)}{F_{m}\left( {{j(s)} + {{e(s)}\frac{M^{2}(D)}{{sL}_{e} + R_{e} + {{RP}\frac{1}{sC}}}}} \right)}}} & (24) \\{{F(s)} = {HR}_{sense}} & (25) \\{{T(s)} = {{AF}.}} & (26)\end{matrix}$

The linear model parameters, e, j, M(D), L_(e), and R_(e) were chosenfor a 500 W buck-derived inverter topology. FIG. 17 shows step responsesof the closed-loop transfer functions in (22) and (23). They showrelatively fast settling times in the input current upon step transientsin the input voltage (corresponding to the string DC bus voltage) andthe reference voltage (corresponding to the control for the sweepableinput current). The lower plot also indicates a significant attenuationof the input current response to changes in the input voltage. Thisattenuation is largely dependent on the low-frequency magnitude of theloop gain T(s) as indicated by equation (22).

5 CONCLUSIONS

Widespread grid penetration of PV relies on the reduction of capitalcost and total cost of ownership for solar power systems. These factorsshould guide the design of photovoltaic power circuits and systemarchitectures. Described herein is a full system approach utilizingswitched capacitor multilevel DC-DC converters. Substantial costreductions may be possible by providing per panel MPPT without the needfor per panel magnetics. Coupling the DC-DC modules with a ripple portinverter can eliminate the need for electrolytic capacitors, enablinglong-life operation. There are tradeoffs among switching frequency,converter efficiency, and global tracking efficiency (I_(o) step size)when considering the dynamics and runtime MPPT approaches for the fullsystem.

Decoupling of the MPPT control among MICs can provide a significantadvantage for these systems so that the MICs can track the power outputof their individual panels despite the actions of the other MICs.Conventional MICs use magnetics-based conversion techniques withcomplicated control circuits that allow them to appear to the string asa current source on the MIC level. By doing so the MIC's can decoupletheir MPPT control from the actions of other MICs.

By contrast, the techniques described herein do not require magneticcomponents. In the absence of magnetic components, the converter may notappear as a current source to the string, and complicated controlcircuit may not be able to remedy this problem. However, by using thesystem level approach described herein, the MICs can be decoupled fromone another even without having the ability to control the MICs to actas a current source to the string. In the system level approachdescribed herein, the central inverter can be input-current-controlledand it can appear as a current sink to all of the MICs. When no magneticcomponents are used in the MICs, using an input-current controlledcentral inverter can restore the ability of the MICs to decouple theirMPPT control, without the need for the MICs to act as current sourcesthemselves.

Using a central inverter that is input-current-controlled enabledecoupling on the MIC level and therefore good tracking efficiencydespite the fundamental limitations of the tracking ability of amultilevel output DC-DC switched capacitor converter. Applying thistechnique to the central inverter can enable good tracking efficiencywithout per panel magnetics, as shown above.

This system level approach can enable efficient use of the multileveloutput DC-DC switched capacitor converter, but use of a multileveloutput DC-DC switched capacitor converter is not required. That is, thesame system level approach that could be used with magnetics-based MIC,which may simpliy the control of the MICs.

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

For example, embodiments of controllers performing maximum power pointtracking, such as controllers 6 and 7, may be implemented usinghardware, software or a combination thereof. When implemented insoftware, the software code can be executed on any suitable hardwareprocessor or collection of hardware processors, whether provided in asingle computer or distributed among multiple computers. It should beappreciated that any component or collection of components that performthe functions described above can be generically considered as one ormore controllers that control the above-discussed functions. The one ormore controllers can be implemented in numerous ways, such as withdedicated hardware, or with general purpose hardware (e.g., one or moreprocessors) that is programmed to perform the functions recited above.

Also, a computer may have one or more input and output devices. Suchcomputers may be interconnected by one or more networks in any suitableform, including a local area network or a wide area network, such as anenterprise network, and intelligent network (IN) or the Internet. Suchnetworks may be based on any suitable technology and may operateaccording to any suitable protocol and may include wireless networks,wired networks or fiber optic networks.

The various methods or processes outlined herein may be coded assoftware that is executable on one or more processors that employ anyone of a variety of operating systems or platforms. Additionally, suchsoftware may be written using any of a number of suitable programminglanguages and/or programming or scripting tools, and also may becompiled as executable machine language code or intermediate code thatis executed on a framework or virtual machine.

In this respect, various inventive concepts may be embodied as acomputer readable storage medium (or multiple computer readable storagemedia) (e.g., a computer memory, one or more floppy discs, compactdiscs, optical discs, magnetic tapes, flash memories, circuitconfigurations in Field Programmable Gate Arrays or other semiconductordevices, or other non-transitory medium or tangible computer storagemedium) encoded with one or more programs that, when executed on one ormore computers or other processors, perform methods that implement thevarious embodiments of the invention discussed above. The computerreadable medium or media can be transportable, such that the program orprograms stored thereon can be loaded onto one or more differentcomputers or other processors to implement various aspects of thepresent invention as discussed above.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of embodiments as discussedabove. Additionally, it should be appreciated that according to oneaspect, one or more computer programs that when executed perform methodsof the present invention need not reside on a single computer orprocessor, but may be distributed in a modular fashion amongst a numberof different computers or processors to implement various aspects of thepresent invention.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, data structures may be stored in computer-readable media in anysuitable form. For simplicity of illustration, data structures may beshown to have fields that are related through location in the datastructure. Such relationships may likewise be achieved by assigningstorage for the fields with locations in a computer-readable medium thatconvey relationship between the fields. However, any suitable mechanismmay be used to establish a relationship between information in fields ofa data structure, including through the use of pointers, tags or othermechanisms that establish relationship between data elements.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The terms “connected” and “coupled” are used interchangeably herein.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively.

1. A circuit for obtaining power from a photovoltaic unit, the circuitcomprising: a DC-DC power converter configured to convert a first signalfrom the photovoltaic unit into a second signal using a conversion ratioselected from a set of discrete conversion ratios that the DC-DC powerconverter is capable of providing.
 2. The circuit of claim 1, whereinthe DC-DC power converter comprises a multi-level output DC-DC switchedcapacitor power converter.
 3. The circuit of claim 2, wherein themulti-level output DC-DC switched capacitor power converter comprises aMarx converter.
 4. The circuit of claim 1, wherein the DC-DC powerconverter does not include a magnetic component.
 5. The circuit of claim1, wherein the set of discrete conversion ratios that the DC-DC powerconverter is capable of providing includes no more than five conversionratios.
 6. The circuit of claim 1, further comprising: a controllerconfigured to control the DC-DC power converter using a maximum powerpoint tracking algorithm.
 7. The circuit of claim 6, whereby the maximumpower point tracking algorithm causes the DC-DC power converter to avoidundervoltage conditions.
 8. The circuit of claim 1, wherein the DC-DCpower converter is configured to enter a bypass mode in which the outputof the DC-DC power converter is connected to panel ground when theconversion ratio is zero.
 9. The circuit of claim 1, wherein the DC-DCpower converter is configured to enter a safety disconnect mode in whichthe input of the DC-DC power converter is disconnected from the outputof the DC-DC power converter by one or more transistors of the DC-DCpower converter, wherein the one or more transistors of the DC-DC powerconverter are configured to switch to provide different conversionratios.
 10. A circuit, comprising: a multi-level output DC-DC switchedcapacitor power converter configured to receive a first signal from aphotovoltaic unit and to convert the first signal into a second signal;and a controller configured to control the multi-level output DC-DCswitched capacitor power converter using a maximum power point trackingalgorithm.
 11. The circuit of claim 10, wherein the multi-level outputDC-DC switched capacitor power converter comprises a Marx converter. 12.The circuit of claim 10, wherein the multi-level output DC-DC switchedcapacitor power converter does not include a magnetic component.
 13. Thecircuit of claim 10, wherein the multi-level output DC-DC switchedcapacitor power converter is capable of providing no more than fiveconversion ratios.
 14. A circuit for controlling a photovoltaic system,the circuit comprising: a plurality of series-connected moduleintegrated converters, each module integrated converter comprising: amulti-level output DC-DC switched capacitor power converter coupled to aphotovoltaic module; and a first controller configured to control themulti-level output DC-DC switched capacitor power converter using amaximum power point tracking algorithm; and an inverter coupled to theplurality of series-connected module integrated converters, the invertercomprising a second controller to control a current through theplurality of series-connected module integrated converters.
 15. Thecircuit of claim 14, wherein the multi-level output DC-DC switchedcapacitor power converter is configured to convert a first signal fromthe photovoltaic module into a second signal using a conversion ratioselected from a set of discrete conversion ratios that the multi-leveloutput DC-DC switched capacitor power converter is capable of providing.16. The circuit of claim 14, wherein the set of discrete conversionratios that the DC-DC power converter is capable of providing includesno more than five conversion ratios.
 17. The circuit of claim 14,wherein the multi-level output DC-DC switched capacitor power convertercomprises a Marx converter.
 18. The circuit of claim 14, wherein theinverter comprises a ripple port inverter.
 19. The circuit of claim 14,wherein the current through the plurality of series-connected moduleintegrated converters is substantially constant.
 20. The circuit ofclaim 14, wherein the first controller is configured to change anoperating point of the photovoltaic module at a first rate and thesecond controller is configured to change the current at a second ratethat is slower than the first rate.
 21. A system for controlling aplurality of photovoltaic units, the system comprising: a first powerconverter coupled to a first photovoltaic unit; a first controller tocontrol the first power converter to operate the first photovoltaic unitusing a maximum power point tracking algorithm; a second power converterin series with the first power converter and coupled to a secondphotovoltaic unit; a second controller to control the second powerconverter to operate the second photovoltaic unit using a maximum powerpoint tracking algorithm; and a third controller that controls a currentthrough the first and second power converters.
 22. The system of claim21, wherein the first power converter comprises a first multi-leveloutput DC-DC switched capacitor power converter and the second powerconverter comprises a second multi-level output DC-DC switched capacitorpower converter.
 23. The system of claim 21, wherein the first powerconverter does not include a magnetic component.
 24. The system of claim21, wherein the first multi-level output DC-DC switched capacitor powerconverter comprises a Marx converter.
 25. The system of claim 21,wherein the third controller controls an inverter to establish thecurrent.
 26. The system of claim 21, wherein the inverter comprises aripple port inverter.
 27. The system of claim 21, wherein the current isa substantially constant current.
 28. The system of claim 21, whereinthe first controller is configured to change an operating point of thefirst photovoltaic unit at a first rate and the third controller isconfigured to change the current at a second rate that is slower thanthe first rate.
 29. The system of claim 21, wherein the firstphotovoltaic unit is a first photovoltaic module and the secondphotovoltaic unit is a second photovoltaic module.
 30. A gate drivecircuit, comprising: a level shift circuit; and a charge pump circuitthat provides a floating gate drive voltage to a transistor of amultilevel output DC-DC switched capacitor power converter based on asignal from the level shift circuit.
 31. The gate drive circuit of claim30, wherein the charge pump circuit comprises an oscillator circuit andthe gate drive circuit further comprises: a zener diode connectedbetween a power terminal of the timer circuit and a source terminal ofthe transistor.
 32. The gate drive circuit of claim 31, furthercomprising a resistive element coupled between the power terminal of thetimer circuit and a terminal that is configured to be grounded.
 33. Thegate drive circuit of claim 32, wherein the resistive element has avariable resistance.
 34. The gate drive circuit of claim 33, wherein thegate drive circuit is configured to select the variable resistance ofthe resistive element at least partially based on a conversion ratio ofthe multilevel output DC-DC switched capacitor power converter.
 35. Thegate drive circuit of claim 34, wherein the gate drive circuit isconfigured to select the variable resistance of the resistive elementfurther based on which transistor of the multilevel output DC-DCswitched capacitor power converter is driven by the floating gate drivevoltage.
 36. The gate drive circuit of claim 32, wherein the resistiveelement comprises a plurality of resistive elements and switches, andwherein the switches are referenced to ground.